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41
Faster scaling algorithms for network problems
 SIAM J. COMPUT
, 1989
"... This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example, the ..."
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Cited by 130 (4 self)
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This paper presents algorithms for the assignment problem, the transportation problem, and the minimumcost flow problem of operations research. The algorithms find a minimumcost solution, yet run in time close to the bestknown bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimumcost matching in a bipartite graph) can be solved in O(v/’rn log(nN)) time, where n, m, and N denote the number of vertices, number of edges, and largest magnitude of a cost; costs are assumed to be integral. The algorithms work by scaling. As in the work of Goldberg and Tarjan, in each scaled problem an approximate optimum solution is found, rather than an exact optimum.
The Complexity of Mean Payoff Games on Graphs
 Theoretical Computer Science
, 1996
"... We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of suc ..."
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Cited by 97 (3 self)
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We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of such games, the decision problem for which is in NP " coNP. Finally, we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by Condon. These games are also known to be in NP " coNP, but no polynomial or pseudopolynomial time algorithm is known for them. 1 Introduction Let G = (V; E)be a finite directed graph in which each vertex has at least one edge going out of it. Let w : E ! f\GammaW; : : : ; 0; : : : ; Wg be a function that assigns an integral weight to each edge of G. Ehrenfeucht and Mycielski [EM79] studied the following infinite twoperson game played on such a graph. The game starts at a vertex a 0 2 V . The first player chooses an edge e...
Faster Maximum and Minimum Mean Cycle Algorithms for System Performance Analysis
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1997
"... Maximum and minimum mean cycle problems are important problems with many applications in performance analysis of synchronous and asynchronous digital systems including rate analysis of embedded systems, in discreteevent systems, and in graph theory. Karp's algorithm is one of the fastest and common ..."
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Cited by 54 (4 self)
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Maximum and minimum mean cycle problems are important problems with many applications in performance analysis of synchronous and asynchronous digital systems including rate analysis of embedded systems, in discreteevent systems, and in graph theory. Karp's algorithm is one of the fastest and commonest algorithms for both of these problems. We present this paper mainly in the context of the maximum mean cycle problem. We show that Karp's algorithm processes more vertices and arcs than needed to find the maximum cycle mean of a digraph. This observation motivated us to propose a new graph unfolding scheme that remedies this deficiency and leads to three faster algorithms with different characteristics. Asymptotic analysis tells us that our algorithms always run faster than Karp's algorithm. Experiments on benchmark graphs confirm this fact for most of the graphs. Like Karp's algorithm, they are also applicable to both the maximum and minimum mean cycle problems. Moreover, one of them is...
Linear Assignment Problems and Extensions
"... This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems ..."
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Cited by 41 (0 self)
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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial threedimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published
An Efficient Cost Scaling Algorithm for the Assignment Problem
 MATH. PROGRAM
, 1995
"... The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the metho ..."
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Cited by 36 (1 self)
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The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
SublinearTime Parallel Algorithms for Matching and Related Problems
, 1988
"... This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial struc ..."
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Cited by 33 (6 self)
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This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial structure of the above problems, which leads to new algorithmic techniques. In particular, we show how to use maximal matching to extend, in parallel, a current set of nodedisjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are "active" during an execution of a pushrelabel network flow algorithm. We also show how to apply our techniques to design parallel algorithms for the weighted versions of the above problems. In particular, we present sublineartime deterministic parallel algorithms for finding a minimumweight bipartite matching and for finding a minimumcost flow in a network with zeroone capacities, if the weights are polynomially ...
Understanding Retiming through Maximum AverageDelay Cycles
 Mathematical Systems Theory
, 1994
"... A synchronous circuit built of functional elements and registers is a simple implementation of the semisystolic model of computation that can be used to design parallel algorithms. Retiming is a wellknown technique that transforms a given circuit into a faster circuit by relocating its registers. W ..."
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Cited by 31 (8 self)
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A synchronous circuit built of functional elements and registers is a simple implementation of the semisystolic model of computation that can be used to design parallel algorithms. Retiming is a wellknown technique that transforms a given circuit into a faster circuit by relocating its registers. We give tight bounds on the minimum clock period that can be achieved by retiming a synchronous circuit. These bounds are expressed in terms of the maximum delaytoregister ratio of the cycles in the circuit graph and the maximum propagation delay d max of the circuit components. Our bounds do not depend on the size of the circuit, and they are of theoretical as well as practical interest. They characterize exactly the minimum clock period that can be achieved by retiming a unitdelay circuit, and they lead to more efficient algorithms for several important problems related to retiming. Specifically, we give an O(V 1=2 E lg V ) algorithm for minimum clock period retiming of unitdelay circu...
Inverse optimization
 OPERATIONS RESEARCH
, 2001
"... In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the c ..."
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Cited by 24 (2 self)
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In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the cost vector c. The inverse optimization problem is to perturb the cost vector c to d so that x 0 is an optimal solution of P with respect to d and �d − c � p is minimum, where �d − c � p is some selected L p norm. In this paper, we consider the inverse linear programming problem under L 1 norm (where �d − c � p = ∑ i∈J w j�d j − c j�, with J denoting the index set of variables x j and w j denoting the weight of the variable j) and under L � norm (where �d −c � p = max j∈J �w j�d j −c j���. We prove the following results: (i) If the problem P is a linear programming problem, then its inverse problem under the L 1 as well as L � norm is also a linear programming problem. (ii) If the problem P is a shortest path, assignment or minimum cut problem, then its inverse problem under the L 1 norm and unit weights can be solved by solving a problem of the same kind. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flow problem. (iii) If the problem P is a minimum cost flowproblem, then its inverse problem under the L 1 norm and unit weights reduces to solving a unitcapacity minimum cost flowproblem. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flowproblem. (iv) If the problem P is a minimum cost flowproblem, then its inverse problem under the L � norm and unit weights reduces to solving a minimum mean cycle problem. For the nonunit weight case, the inverse problem reduces to solving a minimum costtotime ratio cycle problem. (v) If the problem P is polynomially solvable for linear cost functions, then inverse versions of P under the L 1 and L � norms are also polynomially solvable.